Question

The pressure of a certain amount of gas is directly proportional to the temperature (measured on the Kelvin scale) and inversely proportional to the volume. A sample of gas at a pressure of 1 atmosphere occupies a volume of 1 cubic meter at a temperature of 249 Kelvin. When heated, the gas expands to twice its volume, but the pressure remains constant. To what temperature is it heated?

Answer 1

The gas is heated to a temperature of 124.5 Kelvin.

Step-by-step explanation:

1. Define variables:

P: Pressure (in atmospheres)

T: Temperature (in Kelvin)

V: Volume (in cubic meters)

2. Use the proportionality relationship:

We know that P is directly proportional to T and inversely proportional to V. We can write this as an equation:

P = k × T / V

where k is a constant of proportionality.

3. Given information:

Initial pressure P₁ = 1 atmosphere

Initial temperature T₁ = 249 Kelvin

Initial volume V₁ = 1 cubic meter

Final volume V₂ = 2 cubic meters

4. Constant pressure:

We are given that the pressure remains constant after heating. This means P₁ = P₂.

5. Solve for the final temperature (T₂):

From the equation, we can write:

P₁ × V₁ × T₂ = P₂ × V₂ × T₁

Substituting the known values:

1 atm × 1 m³ × T₂ = 1 atm × 2 m³ × 249 K

T2 = (1 atm × 1 m³ × 249 K) / (1 atm × 2 m³)

T2 = 124.5 K

Therefore, the gas is heated to a temperature of 124.5 Kelvin.